Transformation elastodynamics and active exterior acoustic cloaking

Graeme W. Milton 1 D. Onofrei Pierre Seppecher 2 Fernando Guevara Vasquez
1 Department of Mathematics
2 IMATH - Institut de Mathématiques de Toulon - EA 2134
Abstract : This chapter consists of three parts. In the first part we recall the elastodynamic equations under coordinate transformations. The idea is to use coordinate transformations to manipulate waves propagating in an elastic material. Then we study the effect of transformations on a mass-spring network model. The transformed networks can be realized with "torque springs", which are introduced here and are springs with a force proportional to the displacement in a direction other than the direction of the spring terminals. Possible homogenizations of the transformed networks are presented, with potential applications to cloaking. In the second and third parts we present cloaking methods that are based on cancelling an incident field using active devices which are exterior to the cloaked region and that do not generate significant fields far away from the devices. In the second part, the exterior cloaking problem for the Laplace equation is reformulated as the problem of polynomial approximation of analytic functions. An explicit solution is given that allows to cloak larger objects at a fixed distance from the cloaking device, compared to previous explicit solutions. In the third part we consider the active exterior cloaking problem for the Helmholtz equation in 3D. Our method uses the Green's formula and an addition theorem for spherical outgoing waves to design devices that mimic the effect of the single and double layer potentials in Green's formula.
Type de document :
Chapitre d'ouvrage
Richard V. Craster, Sébastien Guenneau. Acoustic Metamaterials, 166, Springer Netherlands, pp.289-319, 2013, Springer Series in Materials Science, 9400748132, 9789400748132
Liste complète des métadonnées
https://hal-univ-tln.archives-ouvertes.fr/hal-01307720
Contributeur : Pierre Seppecher <>
Soumis le : mardi 26 avril 2016 - 16:41:00
Dernière modification le : mardi 19 juin 2018 - 15:50:01

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  • HAL Id : hal-01307720, version 1
  • ARXIV : 1105.1221

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Graeme W. Milton, D. Onofrei, Pierre Seppecher, Fernando Guevara Vasquez. Transformation elastodynamics and active exterior acoustic cloaking. Richard V. Craster, Sébastien Guenneau. Acoustic Metamaterials, 166, Springer Netherlands, pp.289-319, 2013, Springer Series in Materials Science, 9400748132, 9789400748132. 〈hal-01307720〉

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